Positron emission tomography is a branch of nuclear medicine in which a positron-emitting radiopharmaceutical is introduced into the body of a patient. As the radiopharmaceutical decays, positrons are generated. More specifically, each of a plurality of positrons reacts with an electron in what is known as a positron annihilation event, thereby generating a pair of coincident gamma photons which travel substantially in opposite directions along a line of coincidence. A gamma photon pair detected within a coincidence interval is ordinarily recorded by the PET scanner as an annihilation event.
In TOF PET imaging, the time within the coincidence interval at which each gamma photon in the coincident pair is detected is also measured. The time-of-flight information provides an indication of the annihilation location of the detected event along the line of coincidence. Data from a plurality of annihilation events is used to reconstruct or create images of the patient or object scanned, typically by using statistical (iterative) or analytical reconstruction algorithms.
TOF PET has become the state of the art for clinical PET imaging. The list-mode-based iterative reconstruction technique is the most popular choice of image reconstruction algorithms for TOF PET due to its capability of using an accurate system model and thus improving the image quality. To avoid the storage of a huge system matrix, list-mode reconstruction can calculate lines of response (LOR) on-the-fly. However, the accuracy of the on-the-fly calculation is limited due to the constraint on image reconstruction time. This has led to a major use of parallel computing techniques such as distributed computing and the use of graphics processing units (GPUs) to help accelerate the processing speed. On the other hand, for better reconstruction, accurate LORs are necessary to model detector physical response, which still can cause a big computational overhead during the on-the-fly calculation, even with GPU acceleration.
Alternatively, one can use a factorized system model to replace the accurate system model without significant performance degradation. A typical factorized system model may have three major components: a detector blurring matrix, a geometrical projection matrix and an image blurring matrix. The geometrical projection matrix provides the mapping from the image space to the projection space. Unlike the accurate system matrix, it might only contain simple pure geometrical LORs, which often have much fewer nonzero elements, and hence is more suited to the on-the-fly calculation. An often-used projector includes the Siddon's raytracer, which performs the line integral along the line segment defined by a pair of crystals.
A detector blurring matrix can be used along with the geometrical projection matrix to form a complete factorized model. Such factorization has been widely adapted with various detector blurring matrices estimated using either Monte Carlo simulations or real point source scans. However, because the detector blurring requires data in the neighboring projection bins, it is not compatible with the list mode data.
An area-simulating-volume (ASV) TOF-OSEM reconstruction algorithm for PET calculates the overlapping area between the tube-of-response (TOR) and an image voxel as the product of two distance ratios in the X-Y plane and Y-Z (or X-Z) plane, and applies this area as the geometric probability in the system matrix. This reconstruction algorithm has been shown to be very close to a full system matrix modeling in terms of lesion contrast recovery and background noise. However, it does not model extra detector response due to photon pair non-colinearity and crystal penetration, and thus does not have sufficient image resolution recovery.
To reduce TOF-PET data size and preserve spatial accuracy of measured coincidence event, list-mode instead of sinogram reconstruction has been used. In list-mode reconstruction, each individual event is processed one at a time. In this case, a PSF kernel modeled in projection space is not convenient to implement, since its neighboring bins are not readily available.